Question

Austin invested $2000 in an account which pays 3% simple interest. Dallas invested $2000 in an account which pays 3% interest compounded annually. Neither person did deposit any additional money nor did he withdraw any money. What is the difference in the account balance between the two students after 15 years? *

Answer 1

$215.93

Explanation:

You want the difference in account balance after 15 years for a $2000 deposit earning 3% simple interest and one earning 3% compounded annually.

Interest formulas

The account balance formulas are ...

A = P(1 +rt) . . . . . . . principal P earning simple interest at rate r for t years

A = P(1 +r)^t . . . . . . principal P earning compound interest

The difference in account balances is ...

∆ = 2000((1 +0.03)^15 -(1 +0.03·15)) = 3115.93 -2900 = 215.93

The account with interest compounded earns $215.93 more in 15 years.

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